Nine-point circle: Difference between revisions
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In [[triangle geometry]], the '''nine-point circle''' is a circle containing nine points of significance to the triangle: the mid-points of the sides; the feet of the [[altitude (geometry)|altitude]]s; the mid-points of the segments from the vertices to the [[orthocentre]]. The centre of the nine-point circle lies on the [[Euler line]]; the radius is half that of the [[circumcircle]]. | In [[triangle geometry]], the '''nine-point circle''' is a circle containing nine points of significance to the triangle: the mid-points of the sides; the feet of the [[altitude (geometry)|altitude]]s; the mid-points of the segments from the vertices to the [[orthocentre]]. The centre of the nine-point circle lies on the [[Euler line]]; the radius is half that of the [[circumcircle]]. | ||
==References== | |||
* {{cite book | author=H.S.M. Coxeter | coauthors=S.L. Greitzer | title=Geometry revisited | series=New Mathematical Library | volume=19 | publisher=[[MAA]] | year=1967 | isbn=0-88385-619-0 }} | |||
Revision as of 16:30, 24 November 2008
In triangle geometry, the nine-point circle is a circle containing nine points of significance to the triangle: the mid-points of the sides; the feet of the altitudes; the mid-points of the segments from the vertices to the orthocentre. The centre of the nine-point circle lies on the Euler line; the radius is half that of the circumcircle.
References
- H.S.M. Coxeter; S.L. Greitzer (1967). Geometry revisited. MAA. ISBN 0-88385-619-0.